OF FORM OF SHIPS UPON THEIR RESISTANCE. 63 
Figs. 32 to 35, Plate 14, show the same curves as above grouped by 
curves of sectional area. For moderate speeds these again show com- 
paratively small variations, but at high speeds the variations while not great 
are appreciable and the results unwelcome. W. Froude many years ago 
laid down the dictum that broadly speaking the U bow and V stern were 
favorable to speed. Now the fuller the water-line aft and the finer ended 
the curve of sectional area the more the stern approaches the V type. Figs. 
28 to 35, Plates 13 and 14, indicate clearly that for usual speeds the V type 
of stern is superior, but scanning Figs. 32 to 35, Plate 14, we find at 
about a speed length coefficient of 0.95 a change in relative positions of the 
curves and in every case the fine water-line aft is the best at high speeds. 
Careful consideration of the figures will, it is believed, warrant the con- 
clusion that the primary factor involved here is water-line fineness, the 
variations with changes in curves of sectional area being subsidiary. There 
is not much to choose between the sterns with fine ended and full ended 
curves of sectional area. Of course in practice we would wish to use with a 
fine water-line aft a fine ended curve of sectional area to avoid a bulbous 
stern. ; 
There remain two questions to be considered; namely, what is the best 
combination of coefficients in the case of each series and how much can we 
affect the resistance by adopting this best combination. Figs. 36 to a1, 
Plates 15 to 20, show contours of residuary resistance in pounds per ton for 
Series No. 29 of longitudinal coefficient 0.60 plotted upon the values of ¢ for 
the sectional area curves and the values of bow water-line coefficient. These 
refer to the 16 models indicated in Table I and not to interchanged bows 
and sterns. 
Figs. 42 to 47, Plates 21 to 26, give similar contours for Series No. 32, 
of longitudinal coefficient 0.64. 
Vv 
The residuary resistances are so small for low speeds, below ie Ow 
that it is hardly feasible to determine reliable contours from them and indeed 
at the higher speeds the residuary resistances do not differ sufficiently to 
allow reliable contours to be drawn without cross fairing out unsystematic 
differences. For Figs. 36 to 41, Plates 15 to 20, from Series No. 29, we see 
that at and below a speed length ratio of 0.9 there appears to be a distinct 
region for minimum residuary resistance, corresponding to quite fine ends on 
the curves of sectional area and to a bow water-line coefficient slightly greater 
than the longitudinal coefficient. Bearing in mind that for Figs. 36 to 41, 
Plates 15 to 20, fine water-lines forward are associated with fine water-lines 
aft we conclude from Figs. 32 to 35, Plate 14, that the minimum results 
